【作者】 肖粤翔；

【导师】 何桢；

【作者基本信息】 天津大学 ， 管理科学与工程， 2004， 硕士

【摘要】 响应曲面方法（RSM）用于解决未知响应曲面的最优值问题。能否得到好的未知曲面近似，是寻找最优解条件的前提。然而，响应曲面是复杂的，我们使用传统的响应曲面方法很容易落入局部极值点当中，它受到初始中心点的影响比较大，而且通常所采用的一阶和二阶多项式不足以完全反映出实际影响因素本身及其交互作用。非参数响应曲面方法是一个好的选择，它能够应付足够复杂的情况，并得到了广泛应用。本文分析了响应曲面方法的三个阶段，然后采用了多阶段的思路来考虑非参数响应曲面方法。首先是可以利用非参数回归的强大的拟合插值能力对整个可行域进行拟合，将试验点均匀分布到整个试验可行域上，这样就能够把整个可行域的响应曲面表示出来，然后对这个曲面的形状进行判断，找出其最优值的可能位置。其次，发展了一种利用回归方程插值的神经网络方法来拟合最优值附近曲面，它既具有回归方程光滑稳定的特点，又具备神经网络很高的回归精度的优点，能够适应各种复杂的曲面，而且不会有过拟合的的缺点。本文针对响应曲面方法的不同阶段，利用非参数方法的工具来分析和计算，形成了多阶段的非参数响应曲面方法，根据实际需要来在响应曲面方法的各个阶段使用传统的试验设计、快速搜索、多项式拟合或者非参数搜索和拟合。最后本文利用了两个例子来说明了多阶段非参数响应曲面方法的求解过程和应用方法，表明该方法是有效的。更多还原

【Abstract】 Response surface methodology (RSM) is used to get the optimal value of unknown response surface.To get a good response surface is very important to find the optimal value. But the surface is often more complex than that we can imagine. The classical RSM will yield a local optimal result, for the sake of the location of the orginal center point. Sometimes the polynomial fitting cannot reflect the high order interaction between the infleunce factors. Nonparametric response surface methodology (NPRSM) is a good tool to deal with the complex problem and can conquer the shortcomings of classical RSM metioned above.The thesis describes the three phases of RSM, which is DOE, data fitting and searching for the optimal value, and tries to make NPRSM analysis in the same way. Firstly, the design of space-filling grid is fit for the nonparametric regression. The nonparametric regression fits the surface well by using the space-filling grid and can easily find the optimal area. Secondly, a regression-based intepolation artificial neural network is developed to fit the optimum area. The regression-based intepolation artificial neural network is steady, precise, and fits complex unknown surface without overfitting like any other usual neural networks. The thesis presents a mulit-phase NPRSM, which can use DOE, polynomial fitting, nonparametric regression, and neural network in different conditions when it is need. At the end of the thesis, two examples are analyzed by the mulit-phase NPRSM and they prove that the method is very effective.更多还原